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Recent innovative application of UFC bridges in Japan Y. Tanaka & A. Ohtake Taisei Corporation, Tokyo, Japan H. Musha & N. Watanabe Taisei Corporation, Tokyo, Japan ABSTRACT: The design and construction technology of UFC bridges in Japan has been advancing in recent 5 years. This paper presents representative recent 3 projects of UFC structures that have been designed and constructed in Japan as well as the innovative technologies that have been applied step by step through the verification due to the fundamental experiments or accumulated construction know-how. First one is Toyota Footbridge that was applied for the first time the dry joint technology. Second one is a 40 m span monorail girder bridge that may be the longest span girder made of concrete. The last project is the mass production of UFC slabs in Haneda Runway D that must be the largest single project in the world in application of UFC. 1 INTRODUCTION A 50 m span Sakata-Mirai Footbridge has been completed for the first time in Sakata City applying U ltra high strength F ibre reinforced C oncrete (here- after referred to as UFC), the brand name of Ductal R in October 2002. Based on this achieved design, construction technology, material test data and struc- tural experiments, "Recommendation for Design and Construction of Ultra High Strength Fibre Rein- forced Concrete Structures, -Draft" (JSCE, 2004) was published in 2004 by Japan Society of Civil En- gineers. The authors have been challenging the technical development of new design method, joint technol- ogy, efficient production methods of pre-cast seg- ments and construction methods on site for various types of UFC structures. In this paper, the represen- tative recent 3 projects of UFC structures are intro- duced featuring the innovated technologies. Fur- thermore, the advantages and disadvantages of UFC structures in Japan based on our experiences of the past projects are discussed. 2 TOYOTA CITY GYMNASIUM FOOTBRIDGE 2.1 Structural features This footbridge is two-span continuous two-box girder with the dimension of 27.96m in length (span length is 22.5m), 4.72m in width and 0.55m in height (Photo. 1). The bottom and the top slab thick- ness is 6cm and the web thickness is 7cm (Fig. 1). A pre-cast segment method has been adopted account Photograph 1. Completion of Toyota City Gymnasium Foot- bridge in 2007. 4500 550 Shear key 7 0 60 60 Figure 1. Match cast section and shear keys. ing for newly developed dry joint method for the preparation of future large projects. The whole struc- ture was divided into 12 pre-cast segments with the length of 1.9~2.5m. 1% parabolic curvature was re- quired in the longitudinal direction. This means the match cast for dry joint should take this curvature into account when manufacturing. The pre-stressing cables were 4 sets of 19s15.2mm external tendons. 2.2 Match cast method for dry joint The fundamental concept of our dry joint is same Fracture Mechanics of Concrete and Concrete Structures - High Performance, Fiber Reinforced Concrete, Special Loadings and Structural Applications- B. H. Oh, et al. (eds) 2010 Korea Concrete Institute, ISBN 978-89-5708-182-2

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Page 1: Recent innovative application of UFC bridges in Japan - IA …framcos.org/FraMCoS-7/13-18.pdf ·  · 2013-04-10Recent innovative application of UFC bridges in Japan Y. Tanaka & A

Recent innovative application of UFC bridges in Japan

Y. Tanaka & A. Ohtake Taisei Corporation, Tokyo, Japan

H. Musha & N. Watanabe Taisei Corporation, Tokyo, Japan ABSTRACT: The design and construction technology of UFC bridges in Japan has been advancing in recent 5 years. This paper presents representative recent 3 projects of UFC structures that have been designed and constructed in Japan as well as the innovative technologies that have been applied step by step through the verification due to the fundamental experiments or accumulated construction know-how. First one is Toyota Footbridge that was applied for the first time the dry joint technology. Second one is a 40 m span monorail girder bridge that may be the longest span girder made of concrete. The last project is the mass production of UFC slabs in Haneda Runway D that must be the largest single project in the world in application of UFC.

1 INTRODUCTION

A 50 m span Sakata-Mirai Footbridge has been completed for the first time in Sakata City applying Ultra high strength Fibre reinforced Concrete (here-after referred to as UFC), the brand name of Ductal○R in October 2002. Based on this achieved design, construction technology, material test data and struc-tural experiments, "Recommendation for Design and Construction of Ultra High Strength Fibre Rein-forced Concrete Structures, -Draft" (JSCE, 2004) was published in 2004 by Japan Society of Civil En-gineers.

The authors have been challenging the technical development of new design method, joint technol-ogy, efficient production methods of pre-cast seg-ments and construction methods on site for various types of UFC structures. In this paper, the represen-tative recent 3 projects of UFC structures are intro-duced featuring the innovated technologies. Fur-thermore, the advantages and disadvantages of UFC structures in Japan based on our experiences of the past projects are discussed.

2 TOYOTA CITY GYMNASIUM FOOTBRIDGE

2.1 Structural features This footbridge is two-span continuous two-box girder with the dimension of 27.96m in length (span length is 22.5m), 4.72m in width and 0.55m in height (Photo. 1). The bottom and the top slab thick-ness is 6cm and the web thickness is 7cm (Fig. 1). A pre-cast segment method has been adopted account

Photograph 1. Completion of Toyota City Gymnasium Foot-bridge in 2007.

4500

550

Shear key

70

6060

Figure 1. Match cast section and shear keys.

ing for newly developed dry joint method for the preparation of future large projects. The whole struc-ture was divided into 12 pre-cast segments with the length of 1.9~2.5m. 1% parabolic curvature was re-quired in the longitudinal direction. This means the match cast for dry joint should take this curvature into account when manufacturing. The pre-stressing cables were 4 sets of 19s15.2mm external tendons.

2.2 Match cast method for dry joint The fundamental concept of our dry joint is same

Fracture Mechanics of Concrete and Concrete Structures -High Performance, Fiber Reinforced Concrete, Special Loadings and Structural Applications- B. H. Oh, et al. (eds)

ⓒ 2010 Korea Concrete Institute, ISBN 978-89-5708-182-2

Page 2: Recent innovative application of UFC bridges in Japan - IA …framcos.org/FraMCoS-7/13-18.pdf ·  · 2013-04-10Recent innovative application of UFC bridges in Japan Y. Tanaka & A

steel reference mould

new segment old segment

mould to adjust folding angle

steel reference mould

Figure 2. Match cast method for dry joint.

heat shrinkage mould

steel core mould steel core mould

bed mouldside mould

pre-cast segment

space holders Figure 3. Manufacture of pre-cast segment.

Photograph 2. Erection of pre-cast segment.

Photograph 3. Dry joint for pre-cast segment.

as the conventional match cast method usually ap-plied for PC bridges so called pre-cast segment method; i.e. the match cast face is glued by epoxy resin and each segment is connected together by pre-stressing. The different aspect from the conventional one is how to fabricate the match cast segment. The shrinkage of the UFC is primarily 400~500µm/m autogenous shrinkage that is much larger than the conventional concrete. The match cast face of the new segment is usually fabricated by arranging the match cast concrete face of the old segment as a mould. However, the match cast face of the old seg-ment must already have had some autogenous shrinkage in case of the UFC and this sequentially causes unmatched segments. Our new fabrication

method for the segments is that a steel end plate ref-erence mould is set on the old segment to keep con-stant the sectional dimensions. The mould of the new segments is set on the old segment remaining the steel end plate reference mould on the old seg-ment. As the steel end reference plate is constant thickness, the match cast faces result in the mirror image (Fig. 2).

Another unique point is that all shear keys on both sides of the matching face (Fig. 1), are couples of concave shapes. These UFC shear keys were manufactured in advance and were installed while dry-joint was proceeding. It is noted cracking risks usually generated around the shear keys for the case of the conventional match cast faces, will not happen for this case.

2.3 Manufacturing and erection of pre-cast segments

The height of two-box girder is too low to handle a conventional interior mould. New interior mould material was developed to easily relief the interior mould. The material for the interior mould acts as shrinking behaviour due to heat, therefore after the secondary heat curing the interior mould can be eas-ily deleted (Fig. 3). The erection of the pre-cast seg-ments was carried out by crane (Photo. 2). After giv-ing a coat of epoxy resin on the matching surface, each pre-cast segment was pressed against the adja-cent segments by traction equipment. The temporary contact pressure on the matching surface was 0.3N/mm2 (Photo. 3).

Photograph 4. Completion of 40m long monorail girder.

3 TOKYO MONORAIL GIRDER

3.1 Structural features of long span girder Tokyo Monorail and Taisei corporations have been carrying out the corporative technical development of a 40m long monorail girder applying the UFC that must be the longest span in the world made of con-crete material (Photo. 4). Because of the length re-

Proceedings of FraMCoS-7, May 23-28, 2010

hThD ∇−= ),(J (1)

The proportionality coefficient D(h,T) is called moisture permeability and it is a nonlinear function of the relative humidity h and temperature T (Bažant & Najjar 1972). The moisture mass balance requires that the variation in time of the water mass per unit volume of concrete (water content w) be equal to the divergence of the moisture flux J

J•∇=∂

∂−

t

w (2)

The water content w can be expressed as the sum

of the evaporable water we (capillary water, water vapor, and adsorbed water) and the non-evaporable (chemically bound) water wn (Mills 1966, Pantazopoulo & Mills 1995). It is reasonable to assume that the evaporable water is a function of relative humidity, h, degree of hydration, αc, and degree of silica fume reaction, αs, i.e. we=we(h,αc,αs) = age-dependent sorption/desorption isotherm (Norling Mjonell 1997). Under this assumption and by substituting Equation 1 into Equation 2 one obtains

nscw

s

ew

c

ew

hh

Dt

h

h

ew

&&& ++∂

=∇•∇+∂

− αα

αα

)(

(3)

where ∂we/∂h is the slope of the sorption/desorption isotherm (also called moisture capacity). The governing equation (Equation 3) must be completed by appropriate boundary and initial conditions.

The relation between the amount of evaporable water and relative humidity is called ‘‘adsorption isotherm” if measured with increasing relativity humidity and ‘‘desorption isotherm” in the opposite case. Neglecting their difference (Xi et al. 1994), in the following, ‘‘sorption isotherm” will be used with reference to both sorption and desorption conditions. By the way, if the hysteresis of the moisture isotherm would be taken into account, two different relation, evaporable water vs relative humidity, must be used according to the sign of the variation of the relativity humidity. The shape of the sorption isotherm for HPC is influenced by many parameters, especially those that influence extent and rate of the chemical reactions and, in turn, determine pore structure and pore size distribution (water-to-cement ratio, cement chemical composition, SF content, curing time and method, temperature, mix additives, etc.). In the literature various formulations can be found to describe the sorption isotherm of normal concrete (Xi et al. 1994). However, in the present paper the semi-empirical expression proposed by Norling Mjornell (1997) is adopted because it

explicitly accounts for the evolution of hydration reaction and SF content. This sorption isotherm reads

( ) ( )( )

( ) ( )⎥⎥

⎢⎢

⎥⎥⎥

⎢⎢⎢

−∞

+

−∞

−=

1110

,1

110

11,

1,,

hcc

ge

scK

hcc

ge

scG

sch

ew

αα

αα

αα

αααα

(4)

where the first term (gel isotherm) represents the physically bound (adsorbed) water and the second term (capillary isotherm) represents the capillary water. This expression is valid only for low content of SF. The coefficient G1 represents the amount of water per unit volume held in the gel pores at 100% relative humidity, and it can be expressed (Norling Mjornell 1997) as

( ) ss

s

vgkc

c

c

vgk

scG αααα +=,1

(5)

where k

cvg and k

svg are material parameters. From the

maximum amount of water per unit volume that can fill all pores (both capillary pores and gel pores), one can calculate K1 as one obtains

( )1

110

110

11

22.0188.00

,1

−⎟⎠

⎞⎜⎝

⎛−∞

⎥⎥⎥

⎢⎢⎢

⎡⎟⎠

⎞⎜⎝

⎛−∞

−−+−

=

hcc

ge

hcc

geGs

ssc

w

scK

αα

αα

αα

αα

(6)

The material parameters k

cvg and k

svg and g1 can

be calibrated by fitting experimental data relevant to free (evaporable) water content in concrete at various ages (Di Luzio & Cusatis 2009b).

2.2 Temperature evolution

Note that, at early age, since the chemical reactions associated with cement hydration and SF reaction are exothermic, the temperature field is not uniform for non-adiabatic systems even if the environmental temperature is constant. Heat conduction can be described in concrete, at least for temperature not exceeding 100°C (Bažant & Kaplan 1996), by Fourier’s law, which reads

T∇−= λq (7)

where q is the heat flux, T is the absolute temperature, and λ is the heat conductivity; in this

Page 3: Recent innovative application of UFC bridges in Japan - IA …framcos.org/FraMCoS-7/13-18.pdf ·  · 2013-04-10Recent innovative application of UFC bridges in Japan Y. Tanaka & A

striction for the case of 40m long monorail girder, three reversed U-shaped girder (hereafter referred to as "rU girder") segments and three bottom slab seg-ments were separately manufactured in the factory, conveyed to the construction site and jointed to-gether by wet joint and dry joint. Three rU girder segments were connected by dry joint, on the other hand three bottom slab segments and rU girders were connected by wet joint. This wet joint for the connection between the bottom slab segments and rU girders has been originally developed through conducting the fundamental experiments applying the perfobond strips (abbreviated to PBL) with cast-

in-situ UFC. It should be noted that the dry joints for rU girders are located in inner side of the span but the wet-joints for bottom slabs are located outside of the dry joint as shown in Figure 4. The tensile stress for the design load of service limit state (SLS) should be less than the first cracking strength (fcr=8N/mm2) except the joint section, however the tensile stress for SLS can not be allowed on both types of joint; i.e. it should be full pre-stressing for those joints. It is therefore possible to reduce the pre-stressing cables compared with the case that the lo-cations of both joints coincide. The section of the dry joint and the wet joint is illustrated in Figure 5 and Figure 6, respectively.

3.2 Experiment of a proto-type 10m long girder Most of the modelling parameters of the proto-type 10m long monorail girder such as girder width, combination of joints and pre-cast segments, surface finishing of top slab and sizes of PBL are identical with the 40m long girder except the total length and the height (Fig. 7). There are two main purposes for the proto-type monorail girder; i.e. one is to confirm the erection and fabrication method for the complex composition of the pre-cast segments, and another is to verify the structural safety including two kinds of joints. The sequential fabrication steps such as pro-duction of segments, match casting, dry joint and wet joint were implemented and evaluated how those effect on the final structural performance. The

(bottom slab-1)

(rU girder-A)unbond multi cable

wet-joint wet-joint wet-joint wet-joint

(bottom slab-2) (bottom slab-3)

dry-jointdry-joint

(rU girder-B) (rU girder-C)20

00

10809082509020910908250901080

40000

13375 13250 13375

Figure 4. Structural composition of pre-cast segments; rU girder-A,B,C and bottom slab-1,2,3 combined with wet-joint and dry-joint.

150

150

shear key

800

940

2000

150

100

wet joint

70

800

940

130

150

1850

2000

50

Figure 5. Dry-joint. Figure 6. Wet-joint.

9960

dry-joint

unbond multi cable3230

1930 4380680 1930 680

wet-joint

1400

32301500

load

(rU girder-A)

940

1400

800

load

(rU girder-B) (rU girder-C)

90909090(bottom slab-1)

dry-joint

wet-joint wet-joint wet-joint

(bottom slab-2) (bottom slab-3)

Figure 7. Structural composition of pre-cast segments and loading set up for proto-type girder.

Proceedings of FraMCoS-7, May 23-28, 2010

hThD ∇−= ),(J (1)

The proportionality coefficient D(h,T) is called moisture permeability and it is a nonlinear function of the relative humidity h and temperature T (Bažant & Najjar 1972). The moisture mass balance requires that the variation in time of the water mass per unit volume of concrete (water content w) be equal to the divergence of the moisture flux J

J•∇=∂

∂−

t

w (2)

The water content w can be expressed as the sum

of the evaporable water we (capillary water, water vapor, and adsorbed water) and the non-evaporable (chemically bound) water wn (Mills 1966, Pantazopoulo & Mills 1995). It is reasonable to assume that the evaporable water is a function of relative humidity, h, degree of hydration, αc, and degree of silica fume reaction, αs, i.e. we=we(h,αc,αs) = age-dependent sorption/desorption isotherm (Norling Mjonell 1997). Under this assumption and by substituting Equation 1 into Equation 2 one obtains

nscw

s

ew

c

ew

hh

Dt

h

h

ew

&&& ++∂

=∇•∇+∂

− αα

αα

)(

(3)

where ∂we/∂h is the slope of the sorption/desorption isotherm (also called moisture capacity). The governing equation (Equation 3) must be completed by appropriate boundary and initial conditions.

The relation between the amount of evaporable water and relative humidity is called ‘‘adsorption isotherm” if measured with increasing relativity humidity and ‘‘desorption isotherm” in the opposite case. Neglecting their difference (Xi et al. 1994), in the following, ‘‘sorption isotherm” will be used with reference to both sorption and desorption conditions. By the way, if the hysteresis of the moisture isotherm would be taken into account, two different relation, evaporable water vs relative humidity, must be used according to the sign of the variation of the relativity humidity. The shape of the sorption isotherm for HPC is influenced by many parameters, especially those that influence extent and rate of the chemical reactions and, in turn, determine pore structure and pore size distribution (water-to-cement ratio, cement chemical composition, SF content, curing time and method, temperature, mix additives, etc.). In the literature various formulations can be found to describe the sorption isotherm of normal concrete (Xi et al. 1994). However, in the present paper the semi-empirical expression proposed by Norling Mjornell (1997) is adopted because it

explicitly accounts for the evolution of hydration reaction and SF content. This sorption isotherm reads

( ) ( )( )

( ) ( )⎥⎥

⎢⎢

⎥⎥⎥

⎢⎢⎢

−∞

+

−∞

−=

1110

,1

110

11,

1,,

hcc

ge

scK

hcc

ge

scG

sch

ew

αα

αα

αα

αααα

(4)

where the first term (gel isotherm) represents the physically bound (adsorbed) water and the second term (capillary isotherm) represents the capillary water. This expression is valid only for low content of SF. The coefficient G1 represents the amount of water per unit volume held in the gel pores at 100% relative humidity, and it can be expressed (Norling Mjornell 1997) as

( ) ss

s

vgkc

c

c

vgk

scG αααα +=,1

(5)

where k

cvg and k

svg are material parameters. From the

maximum amount of water per unit volume that can fill all pores (both capillary pores and gel pores), one can calculate K1 as one obtains

( )1

110

110

11

22.0188.00

,1

−⎟⎠

⎞⎜⎝

⎛−∞

⎥⎥⎥

⎢⎢⎢

⎡⎟⎠

⎞⎜⎝

⎛−∞

−−+−

=

hcc

ge

hcc

geGs

ssc

w

scK

αα

αα

αα

αα

(6)

The material parameters k

cvg and k

svg and g1 can

be calibrated by fitting experimental data relevant to free (evaporable) water content in concrete at various ages (Di Luzio & Cusatis 2009b).

2.2 Temperature evolution

Note that, at early age, since the chemical reactions associated with cement hydration and SF reaction are exothermic, the temperature field is not uniform for non-adiabatic systems even if the environmental temperature is constant. Heat conduction can be described in concrete, at least for temperature not exceeding 100°C (Bažant & Kaplan 1996), by Fourier’s law, which reads

T∇−= λq (7)

where q is the heat flux, T is the absolute temperature, and λ is the heat conductivity; in this

Page 4: Recent innovative application of UFC bridges in Japan - IA …framcos.org/FraMCoS-7/13-18.pdf ·  · 2013-04-10Recent innovative application of UFC bridges in Japan Y. Tanaka & A

Photograph 5. rU girder segment.

0

500

1000

1500

2000

2500

0 5 10 15 20 25 30Displacement δ (mm)

Load

 P 

(kN

)

EXP.FEMULS P=1748kNSLS P=830kN

Figure 8. Comparison of loading experiment and FEM analysis.

rU girder segment is lifted to assemble with the rest of the segments as illustrated in Photograph 5 where the match cast face with concave shear keys and PBL inserted in the segment for wet joint with bot-tom slab are observed.

The loading set up for the completed proto-type girder was arranged so that both joints could have both bending moment and shear force (Fig. 7). The experimental result and a 3D-FEM analysis consid-ered the modelling of material nonlinearity is indi-cated in Figure 8. Because a 10m long monorail girder instead of a 40m girder was to be tested to prove the structural safety, the equivalent loading values were calculated so as to have equivalent forces at joints for SLS and ULS. The loading value P for SLS and ULS became 830kN and 1748kN, re-spectively. It was proven that no initial cracking was observed for SLS and no serious damage for ULS. The first cracking was observed at the bottom slab of mid-span for the loading value P=1200~1300kN. At the same time, the first cracking at wet joint of bot-tom slab was found. For the loading value P=1700kN, the diagonal cracks were observed on web.

Photo. 6. Bottom slab. Photograph 7. r-U girder.

3.3 Fabrication of a 40m long girder Three rU girder segments and three bottom slab segments were manufactured and conveyed to the construction site. Three bottom segments with PBL were settled on the levelled supporting beams (Photo. 6). Three rU girder segments with four ad-justable legs were erected on the bottom segments at 10cm above the final level (Photo. 7). After giving a coat of epoxy resin on the matching surface, each rU girder segment was pressed against the adjacent segments by traction equipment. The temporary con-tact pressure on the matching surface was 0.3N/mm2 and those dry jointed segments were set down about 10cm ready to the subsequent wet joint step. As a wet joint step, 1) cast-in-situ UFC was placed into the space between the web and the bottom slab as well as into the space between bottom slabs, 2) heat curing was carried out keeping the atmosphere tem-perature 60oC for 48 hours. After the compressive strength of wet joint cast-in-situ UFC reaching up to at least 160 N/mm2, the pre-stressing step has been progressed to supply the design stresses not only on the dry joint but also on the wet joint. It should be noted that the top slab surface and the side web sur-face of the dry joint were finished extremely smooth.

4 PLATFORM SLABS IN HANEDA RUNWAY D

4.1 UFC slabs in Haneda Runway D The construction of Runway D is a national project of the extension of the Haneda International Airport, Tokyo. About one third of Runway D is composed of the pile-elevated platform and the rest of it is composed of the reclaimed land. The reason why such a complex structure was adopted is to avoid blocking the river flow of Tama River. The outside area (blue area in Fig. 9) of the pile-elevated plat-form is made from pre-cast slabs applying UFC. The area of this part is 192,000m2 and about 6.900 pieces

Proceedings of FraMCoS-7, May 23-28, 2010

hThD ∇−= ),(J (1)

The proportionality coefficient D(h,T) is called moisture permeability and it is a nonlinear function of the relative humidity h and temperature T (Bažant & Najjar 1972). The moisture mass balance requires that the variation in time of the water mass per unit volume of concrete (water content w) be equal to the divergence of the moisture flux J

J•∇=∂

∂−

t

w (2)

The water content w can be expressed as the sum

of the evaporable water we (capillary water, water vapor, and adsorbed water) and the non-evaporable (chemically bound) water wn (Mills 1966, Pantazopoulo & Mills 1995). It is reasonable to assume that the evaporable water is a function of relative humidity, h, degree of hydration, αc, and degree of silica fume reaction, αs, i.e. we=we(h,αc,αs) = age-dependent sorption/desorption isotherm (Norling Mjonell 1997). Under this assumption and by substituting Equation 1 into Equation 2 one obtains

nscw

s

ew

c

ew

hh

Dt

h

h

ew

&&& ++∂

=∇•∇+∂

− αα

αα

)(

(3)

where ∂we/∂h is the slope of the sorption/desorption isotherm (also called moisture capacity). The governing equation (Equation 3) must be completed by appropriate boundary and initial conditions.

The relation between the amount of evaporable water and relative humidity is called ‘‘adsorption isotherm” if measured with increasing relativity humidity and ‘‘desorption isotherm” in the opposite case. Neglecting their difference (Xi et al. 1994), in the following, ‘‘sorption isotherm” will be used with reference to both sorption and desorption conditions. By the way, if the hysteresis of the moisture isotherm would be taken into account, two different relation, evaporable water vs relative humidity, must be used according to the sign of the variation of the relativity humidity. The shape of the sorption isotherm for HPC is influenced by many parameters, especially those that influence extent and rate of the chemical reactions and, in turn, determine pore structure and pore size distribution (water-to-cement ratio, cement chemical composition, SF content, curing time and method, temperature, mix additives, etc.). In the literature various formulations can be found to describe the sorption isotherm of normal concrete (Xi et al. 1994). However, in the present paper the semi-empirical expression proposed by Norling Mjornell (1997) is adopted because it

explicitly accounts for the evolution of hydration reaction and SF content. This sorption isotherm reads

( ) ( )( )

( ) ( )⎥⎥

⎢⎢

⎥⎥⎥

⎢⎢⎢

−∞

+

−∞

−=

1110

,1

110

11,

1,,

hcc

ge

scK

hcc

ge

scG

sch

ew

αα

αα

αα

αααα

(4)

where the first term (gel isotherm) represents the physically bound (adsorbed) water and the second term (capillary isotherm) represents the capillary water. This expression is valid only for low content of SF. The coefficient G1 represents the amount of water per unit volume held in the gel pores at 100% relative humidity, and it can be expressed (Norling Mjornell 1997) as

( ) ss

s

vgkc

c

c

vgk

scG αααα +=,1

(5)

where k

cvg and k

svg are material parameters. From the

maximum amount of water per unit volume that can fill all pores (both capillary pores and gel pores), one can calculate K1 as one obtains

( )1

110

110

11

22.0188.00

,1

−⎟⎠

⎞⎜⎝

⎛−∞

⎥⎥⎥

⎢⎢⎢

⎡⎟⎠

⎞⎜⎝

⎛−∞

−−+−

=

hcc

ge

hcc

geGs

ssc

w

scK

αα

αα

αα

αα

(6)

The material parameters k

cvg and k

svg and g1 can

be calibrated by fitting experimental data relevant to free (evaporable) water content in concrete at various ages (Di Luzio & Cusatis 2009b).

2.2 Temperature evolution

Note that, at early age, since the chemical reactions associated with cement hydration and SF reaction are exothermic, the temperature field is not uniform for non-adiabatic systems even if the environmental temperature is constant. Heat conduction can be described in concrete, at least for temperature not exceeding 100°C (Bažant & Kaplan 1996), by Fourier’s law, which reads

T∇−= λq (7)

where q is the heat flux, T is the absolute temperature, and λ is the heat conductivity; in this

Page 5: Recent innovative application of UFC bridges in Japan - IA …framcos.org/FraMCoS-7/13-18.pdf ·  · 2013-04-10Recent innovative application of UFC bridges in Japan Y. Tanaka & A

Runway D

Taxiway

UFC slab area(blue area)

Figure 9. Allocation of UFC slabs on Haneda Runway D.

Figure 10. Structural detail of UFC slab and joint with steel girder.

of UFC slabs were applied. The reasons for applying UFC to the deck slabs were as follows; 1) Applica-tion of the UFC material to the deck slabs made it possible to realize the reduction in self weight of deck slabs by 56% compared to the ordinary con-crete slabs. As a result, the weight of the steel jacket and the steel piles could be decreased so the con-struction cost could be reduced. 2) The UFC material is extremely durable so the maintenance cost must be reduced. 3) In September 2004, the UFC Rec-ommendation (JSCE, 2004) was published by JSCE, so it became possible to conduct the objective check of the required performance.

4.2 Structural features of UFC slabs The principal direction of the slab coincides with the direction of the shorter side and the ribs are set along the principal direction (Fig. 10). The height includ-ing the ribs is 250mm and the thinnest thickness of the UFC slab is only 75mm. The averaged slab thickness is about 135mm on the other hand the or-dinary concrete slab thickness with compressive strength 50N/mm2 becomes 320mm. This means the reduction in dead load compared with the ordinary concrete slab is about 56% (Table 1). One of the fea-turing points of the UFC slabs is the adoption of the two-directional pre-tensioning newly developed technology in order to efficiently produce a huge amount of the UFC slabs. There was no precedent such a two-directional pre-tensioning method for manufacturing the slabs, however this method was more advantageous from the cost point of view than the usual method, i.e. pre-tensioning in one direction and post-tensioning in one direction.

The design load for each limit state is as follows; 1) SLS (normal condition) --slab dead load + vehicle loading, 2) ULS (emergency condition) --slab dead load + aircraft loading (aircraft deviating from the runway and taxiway). The items checked for SLS are the tensile and compressive stress should be less than -8.0N/mm2 and 108N/mm2, respectively. Those for ULS are factor of safety against collapse should be greater than one and the stress in pre-stressing steel should be less than yield stress. Particularly in the case of aircraft running, it was required that there would be limited damage so that the slabs could be subsequently used. In order to satisfy these condi-tions, the limiting state was imposed that the stress in the pre-stressing steel should be less than the yield stress when aircraft loading is applied. The UFC slabs are simply supported on the frame of the jacket platform. Three-dimensional FEM analyses includ-ing the jacket frame model was applied to calculate the stresses in the slabs and it resulted in that all stress responses and all final limiting states for SLS and ULS satisfied the design items.

4.3 Loading tests using full scale UFC slabs The loading tests using full scale UFC slabs were conducted in order to confirm that 1) the response stresses and loading bearing capacity could be ob-tained in accordance with the UFC slab design cal-culations, 2) the production system such as material, formwork, casting, curing, pre-stressing, de-moulding and fiber orientation to manufacture the UFC slabs could be stably under quality control. The loading tests were carried out on two specimens in order to clarify the variation due to the UFC material and due to manufacturing system. In the tests, the vehicle loading was firstly applied three repeated

in principal direction

in lateral directionPC tendon 1S15.2

250

75

PC tendon 1S19.3

Waterproofing coating

UFC slab

Steel girder

Joint concrete

pavement

stud dowel

62

UFC slab

250 joint concrete

40

steel girderjoint mortar

Proceedings of FraMCoS-7, May 23-28, 2010

hThD ∇−= ),(J (1)

The proportionality coefficient D(h,T) is called moisture permeability and it is a nonlinear function of the relative humidity h and temperature T (Bažant & Najjar 1972). The moisture mass balance requires that the variation in time of the water mass per unit volume of concrete (water content w) be equal to the divergence of the moisture flux J

J•∇=∂

∂−

t

w (2)

The water content w can be expressed as the sum

of the evaporable water we (capillary water, water vapor, and adsorbed water) and the non-evaporable (chemically bound) water wn (Mills 1966, Pantazopoulo & Mills 1995). It is reasonable to assume that the evaporable water is a function of relative humidity, h, degree of hydration, αc, and degree of silica fume reaction, αs, i.e. we=we(h,αc,αs) = age-dependent sorption/desorption isotherm (Norling Mjonell 1997). Under this assumption and by substituting Equation 1 into Equation 2 one obtains

nscw

s

ew

c

ew

hh

Dt

h

h

ew

&&& ++∂

=∇•∇+∂

− αα

αα

)(

(3)

where ∂we/∂h is the slope of the sorption/desorption isotherm (also called moisture capacity). The governing equation (Equation 3) must be completed by appropriate boundary and initial conditions.

The relation between the amount of evaporable water and relative humidity is called ‘‘adsorption isotherm” if measured with increasing relativity humidity and ‘‘desorption isotherm” in the opposite case. Neglecting their difference (Xi et al. 1994), in the following, ‘‘sorption isotherm” will be used with reference to both sorption and desorption conditions. By the way, if the hysteresis of the moisture isotherm would be taken into account, two different relation, evaporable water vs relative humidity, must be used according to the sign of the variation of the relativity humidity. The shape of the sorption isotherm for HPC is influenced by many parameters, especially those that influence extent and rate of the chemical reactions and, in turn, determine pore structure and pore size distribution (water-to-cement ratio, cement chemical composition, SF content, curing time and method, temperature, mix additives, etc.). In the literature various formulations can be found to describe the sorption isotherm of normal concrete (Xi et al. 1994). However, in the present paper the semi-empirical expression proposed by Norling Mjornell (1997) is adopted because it

explicitly accounts for the evolution of hydration reaction and SF content. This sorption isotherm reads

( ) ( )( )

( ) ( )⎥⎥

⎢⎢

⎥⎥⎥

⎢⎢⎢

−∞

+

−∞

−=

1110

,1

110

11,

1,,

hcc

ge

scK

hcc

ge

scG

sch

ew

αα

αα

αα

αααα

(4)

where the first term (gel isotherm) represents the physically bound (adsorbed) water and the second term (capillary isotherm) represents the capillary water. This expression is valid only for low content of SF. The coefficient G1 represents the amount of water per unit volume held in the gel pores at 100% relative humidity, and it can be expressed (Norling Mjornell 1997) as

( ) ss

s

vgkc

c

c

vgk

scG αααα +=,1

(5)

where k

cvg and k

svg are material parameters. From the

maximum amount of water per unit volume that can fill all pores (both capillary pores and gel pores), one can calculate K1 as one obtains

( )1

110

110

11

22.0188.00

,1

−⎟⎠

⎞⎜⎝

⎛−∞

⎥⎥⎥

⎢⎢⎢

⎡⎟⎠

⎞⎜⎝

⎛−∞

−−+−

=

hcc

ge

hcc

geGs

ssc

w

scK

αα

αα

αα

αα

(6)

The material parameters k

cvg and k

svg and g1 can

be calibrated by fitting experimental data relevant to free (evaporable) water content in concrete at various ages (Di Luzio & Cusatis 2009b).

2.2 Temperature evolution

Note that, at early age, since the chemical reactions associated with cement hydration and SF reaction are exothermic, the temperature field is not uniform for non-adiabatic systems even if the environmental temperature is constant. Heat conduction can be described in concrete, at least for temperature not exceeding 100°C (Bažant & Kaplan 1996), by Fourier’s law, which reads

T∇−= λq (7)

where q is the heat flux, T is the absolute temperature, and λ is the heat conductivity; in this

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Photograph 8. Full scale loading experiment of UFC slab.

times and then the aircraft loading was secondary applied two repeated times. Then finally the loading in excess of the aircraft loading was applied (Photo. 8). The wheel loading position (six wheels on one UFC slab) was determined in accordance with the wheel layout of the aircraft B777-200ER where the ultimate cross-sectional forces were most severe. The UFC slabs would be actually supported on the flexible steel frames of the steel jacket but the sup

0

100

200

300

400

500

600

700

-50-40-30-20-100

displacement (mm)

Load

(kN

/w

heel

)FEM with lower limitFEM with upper limit

Equiv. vehicle(short dir.)

Equiv. Vehicle load (long dir.)194kN/wheel

Equv. Aircraft load 321kN/wheel

Flexural bearing load501kN/wheel

Exp. aircraft

Exp.vehicle

Figure 11. Comparison of experiment and FEM analysis.

port condition of the loading tests was obliged to be rigid. Therefore the equivalent loads were set to re-produce the cross-sectional forces and stresses calcu-lated during the design.

The loading test results of the load per wheel ver-sus the displacement at the centre of the specimen and three-dimensional FEM analyses taking the UFC material nonlinearity into account are compared with each other in Figure 11. The displace

Table 1. Comparison of UFC slab and conventional concrete slab.

UFC Slab Conventional Concrete Slab

Average thickness=135 mm Average thickness=320 mm

unit dead load=3.83 kN/m2 unit dead load=7.84 kN/m2

W = 97 kN/slab W =221 kN/slab

17500 104500 41500 36500

45000

200000

Steel wire

Stockyard

Pre-tensionning abutment

Haul road

Haul road

Production yard (pouring and first curing)Wire end processing areaInspection areaSecondary curing yard

UFC slab (20 slabs per line) Steam curing tank

ProductionLine A

ProductionLine B

Steel wire

Figure 12. Layout plan of UFC slab factory.

Proceedings of FraMCoS-7, May 23-28, 2010

hThD ∇−= ),(J (1)

The proportionality coefficient D(h,T) is called moisture permeability and it is a nonlinear function of the relative humidity h and temperature T (Bažant & Najjar 1972). The moisture mass balance requires that the variation in time of the water mass per unit volume of concrete (water content w) be equal to the divergence of the moisture flux J

J•∇=∂

∂−

t

w (2)

The water content w can be expressed as the sum

of the evaporable water we (capillary water, water vapor, and adsorbed water) and the non-evaporable (chemically bound) water wn (Mills 1966, Pantazopoulo & Mills 1995). It is reasonable to assume that the evaporable water is a function of relative humidity, h, degree of hydration, αc, and degree of silica fume reaction, αs, i.e. we=we(h,αc,αs) = age-dependent sorption/desorption isotherm (Norling Mjonell 1997). Under this assumption and by substituting Equation 1 into Equation 2 one obtains

nscw

s

ew

c

ew

hh

Dt

h

h

ew

&&& ++∂

=∇•∇+∂

− αα

αα

)(

(3)

where ∂we/∂h is the slope of the sorption/desorption isotherm (also called moisture capacity). The governing equation (Equation 3) must be completed by appropriate boundary and initial conditions.

The relation between the amount of evaporable water and relative humidity is called ‘‘adsorption isotherm” if measured with increasing relativity humidity and ‘‘desorption isotherm” in the opposite case. Neglecting their difference (Xi et al. 1994), in the following, ‘‘sorption isotherm” will be used with reference to both sorption and desorption conditions. By the way, if the hysteresis of the moisture isotherm would be taken into account, two different relation, evaporable water vs relative humidity, must be used according to the sign of the variation of the relativity humidity. The shape of the sorption isotherm for HPC is influenced by many parameters, especially those that influence extent and rate of the chemical reactions and, in turn, determine pore structure and pore size distribution (water-to-cement ratio, cement chemical composition, SF content, curing time and method, temperature, mix additives, etc.). In the literature various formulations can be found to describe the sorption isotherm of normal concrete (Xi et al. 1994). However, in the present paper the semi-empirical expression proposed by Norling Mjornell (1997) is adopted because it

explicitly accounts for the evolution of hydration reaction and SF content. This sorption isotherm reads

( ) ( )( )

( ) ( )⎥⎥

⎢⎢

⎥⎥⎥

⎢⎢⎢

−∞

+

−∞

−=

1110

,1

110

11,

1,,

hcc

ge

scK

hcc

ge

scG

sch

ew

αα

αα

αα

αααα

(4)

where the first term (gel isotherm) represents the physically bound (adsorbed) water and the second term (capillary isotherm) represents the capillary water. This expression is valid only for low content of SF. The coefficient G1 represents the amount of water per unit volume held in the gel pores at 100% relative humidity, and it can be expressed (Norling Mjornell 1997) as

( ) ss

s

vgkc

c

c

vgk

scG αααα +=,1

(5)

where k

cvg and k

svg are material parameters. From the

maximum amount of water per unit volume that can fill all pores (both capillary pores and gel pores), one can calculate K1 as one obtains

( )1

110

110

11

22.0188.00

,1

−⎟⎠

⎞⎜⎝

⎛−∞

⎥⎥⎥

⎢⎢⎢

⎡⎟⎠

⎞⎜⎝

⎛−∞

−−+−

=

hcc

ge

hcc

geGs

ssc

w

scK

αα

αα

αα

αα

(6)

The material parameters k

cvg and k

svg and g1 can

be calibrated by fitting experimental data relevant to free (evaporable) water content in concrete at various ages (Di Luzio & Cusatis 2009b).

2.2 Temperature evolution

Note that, at early age, since the chemical reactions associated with cement hydration and SF reaction are exothermic, the temperature field is not uniform for non-adiabatic systems even if the environmental temperature is constant. Heat conduction can be described in concrete, at least for temperature not exceeding 100°C (Bažant & Kaplan 1996), by Fourier’s law, which reads

T∇−= λq (7)

where q is the heat flux, T is the absolute temperature, and λ is the heat conductivity; in this

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Photograph 9. UFC slab factory.

Photograph 10. UFC batching plant.

ments under the repetition of vehicle loading due to SLS demonstrated linearity and there were no sig-nificant residual displacement. The first crack was observed in the beam in the short direction at the stage when the load slightly exceeded 200kN. There was no significant difference between the behaviour under the 1st and 3rd loads at the equivalent aircraft load (321kN/wheel). The crack width was only 0.1mm or less under a load (600kN/wheel) in excess of the bending collapse load (501kN/wheel) based on the design calculation. In order to confirm that the variation in the two tests results were within the postulated range, the input data for FEM model were set to be upper and lower limits on the variation in the material quality postulated for the production of the actual slabs. The tests results were within the up-per and lower limits FEM results. In addition two test results due to two specimens respectively were almost same therefore it can be concluded that the variation in the slabs is very small.

4.4 Production of the UFC slabs The production factory for the UFC slabs was newly constructed in Footsu City in Chiba Prefecture. As shown in the factory layout plan of Figure 12, the factory is equipped with two-directional pre-tensioning abutments which can not be seen in the

Photograph 11. Slab production line.

Photograph 12. Casting UFC to mould.

world and this factory to produce the UFC material must be the world's largest. The roofed area of the factory had a width of 45m and a length of 200m (Photo. 9). There are two lines, A and B, and each line had its own production yard, secondary curing tank, pre-stressing steel end processing area, and in-spection area. A dedicated UFC batching plant capa-ble of mixing 15m3 per hour was installed within the factory site (Photo. 10), and can produce 70m3 of UFC (quantity of 20 slabs) in 5 hours. In the produc-tion yard of each line, concrete abutments were pro-vided for pre-tensioning, and 20 sets of formwork were provided within the abutments (Photo. 11). The UFC mixed in the batching plant is transported to the production yards, where it is poured into the formwork with the pre-tensioning cables in two di-rections (Photo. 12).

On the following morning after it has been con-firmed that the strength exceeded 45N/mm2, the pre-stressing is introduced, the pre-stressing tendons are cut, and the slabs are transported to the secondary curing tank by a gantry crane. Three secondary cur-ing tanks were provided per line, based on consid-erations of the production cycle. The UFC slabs transported from the production yards are placed

Proceedings of FraMCoS-7, May 23-28, 2010

hThD ∇−= ),(J (1)

The proportionality coefficient D(h,T) is called moisture permeability and it is a nonlinear function of the relative humidity h and temperature T (Bažant & Najjar 1972). The moisture mass balance requires that the variation in time of the water mass per unit volume of concrete (water content w) be equal to the divergence of the moisture flux J

J•∇=∂

∂−

t

w (2)

The water content w can be expressed as the sum

of the evaporable water we (capillary water, water vapor, and adsorbed water) and the non-evaporable (chemically bound) water wn (Mills 1966, Pantazopoulo & Mills 1995). It is reasonable to assume that the evaporable water is a function of relative humidity, h, degree of hydration, αc, and degree of silica fume reaction, αs, i.e. we=we(h,αc,αs) = age-dependent sorption/desorption isotherm (Norling Mjonell 1997). Under this assumption and by substituting Equation 1 into Equation 2 one obtains

nscw

s

ew

c

ew

hh

Dt

h

h

ew

&&& ++∂

=∇•∇+∂

− αα

αα

)(

(3)

where ∂we/∂h is the slope of the sorption/desorption isotherm (also called moisture capacity). The governing equation (Equation 3) must be completed by appropriate boundary and initial conditions.

The relation between the amount of evaporable water and relative humidity is called ‘‘adsorption isotherm” if measured with increasing relativity humidity and ‘‘desorption isotherm” in the opposite case. Neglecting their difference (Xi et al. 1994), in the following, ‘‘sorption isotherm” will be used with reference to both sorption and desorption conditions. By the way, if the hysteresis of the moisture isotherm would be taken into account, two different relation, evaporable water vs relative humidity, must be used according to the sign of the variation of the relativity humidity. The shape of the sorption isotherm for HPC is influenced by many parameters, especially those that influence extent and rate of the chemical reactions and, in turn, determine pore structure and pore size distribution (water-to-cement ratio, cement chemical composition, SF content, curing time and method, temperature, mix additives, etc.). In the literature various formulations can be found to describe the sorption isotherm of normal concrete (Xi et al. 1994). However, in the present paper the semi-empirical expression proposed by Norling Mjornell (1997) is adopted because it

explicitly accounts for the evolution of hydration reaction and SF content. This sorption isotherm reads

( ) ( )( )

( ) ( )⎥⎥

⎢⎢

⎥⎥⎥

⎢⎢⎢

−∞

+

−∞

−=

1110

,1

110

11,

1,,

hcc

ge

scK

hcc

ge

scG

sch

ew

αα

αα

αα

αααα

(4)

where the first term (gel isotherm) represents the physically bound (adsorbed) water and the second term (capillary isotherm) represents the capillary water. This expression is valid only for low content of SF. The coefficient G1 represents the amount of water per unit volume held in the gel pores at 100% relative humidity, and it can be expressed (Norling Mjornell 1997) as

( ) ss

s

vgkc

c

c

vgk

scG αααα +=,1

(5)

where k

cvg and k

svg are material parameters. From the

maximum amount of water per unit volume that can fill all pores (both capillary pores and gel pores), one can calculate K1 as one obtains

( )1

110

110

11

22.0188.00

,1

−⎟⎠

⎞⎜⎝

⎛−∞

⎥⎥⎥

⎢⎢⎢

⎡⎟⎠

⎞⎜⎝

⎛−∞

−−+−

=

hcc

ge

hcc

geGs

ssc

w

scK

αα

αα

αα

αα

(6)

The material parameters k

cvg and k

svg and g1 can

be calibrated by fitting experimental data relevant to free (evaporable) water content in concrete at various ages (Di Luzio & Cusatis 2009b).

2.2 Temperature evolution

Note that, at early age, since the chemical reactions associated with cement hydration and SF reaction are exothermic, the temperature field is not uniform for non-adiabatic systems even if the environmental temperature is constant. Heat conduction can be described in concrete, at least for temperature not exceeding 100°C (Bažant & Kaplan 1996), by Fourier’s law, which reads

T∇−= λq (7)

where q is the heat flux, T is the absolute temperature, and λ is the heat conductivity; in this

Page 8: Recent innovative application of UFC bridges in Japan - IA …framcos.org/FraMCoS-7/13-18.pdf ·  · 2013-04-10Recent innovative application of UFC bridges in Japan Y. Tanaka & A

within one of the curing tanks, and steam curing is carried out at 90oC for 48 hours.

5 CONCLUSIONS

Starting from Sakata-Mirai Footbridge in 2002, the authors have been developing the innovative design and construction technologies such as wet joint, dry joint, PBL joint, non-linear FEM analyses consider-ing UFC tension softening and efficient manufactur-ing methods. In this paper, three typical innovative application projects of UFC bridges were introduced and the following conclusions are derived from those projects.

In the Toyota City Gymnasium Footbridge pro-ject, the match cast method for dry joint applying the UFC material was developed for the first time. Through applying a steel end plate reference mould to keep the sectional dimensions of the old segment, all pre-cast segments could be accurately manufac-tured and could be quickly jointed together only giv-ing the a coat of epoxy resin on the matching sur-face. This joint method enabled the site construction time 1/3 compared with the conventional wet joint method. The wet joint method that the UFC material was poured into the 30mm gaps was developed in the Sakata-Mirai Footbridge project. Therefore, the accurate matching surface configuration of the seg-ments is not required but the long construction pe-riod on site is required for the sake of the heat curing for the UFC joint material. In case of the Toyota pro-ject, 12 construction days for wet joint was reduced to 4 construction days for dry joint. This dry joint technology will be applied in the future for the large-scale pre-cast segments method for the construction of the long span highway bridges.

Tokyo Monorail girder was successfully com-pleted as a result of structural verification of a series of experiments as well as the functional verification such as accurate configuration of the top slab surface for the rubber wheel running. It should be noted that the combination of the dry joint and the wet PBL joint was unique and effective, i.e. the different posi-tion between the dry joint for three rU girder seg-ments and the wet PBL joint for the connection be-tween the bottom slab segments must make reduce the pre-stressing cables. The three dimensional FEM analysis considering the modeling of material nonlinearity could well predict the loading experi-ments results of the proto-type 10m long monorail girder including the wet and dry joints. One of the key points of the modeling the material nonlinearity was the tension softening diagrams for the UFC ma-terial.

The most successful applications of the UFC ma-terial to the bridge structures is the construction of the UFC slabs for the pile-elevated platform in

Haneda Runway D. The UFC pre-cast slabs were se-lected as the best cost-performance structures pro-vided that the load tests using full sized UFC slabs could confirm that the response and load resistance could be obtained in accordance with the UFC slab design calculations. The conclusions regarding the design of the UFC slabs based on the results of the loading tests carried out using two full size speci-mens are 1) cracking does not occur at the SLS, 2) at the ULS (aircraft load) emergency replacement or repair will not be necessary, 3) the maximum load bearing capacity has sufficient margin with respect to the aircraft loading and 4) three-dimensional FEM analyses taking the UFC material nonlinearity into account can well predict the nonlinear behavior and are confirmed as a design tool. It should be noted that the key points of the success of the UFC slabs should be 1) total cost saving due to the enormous reduction of the slabs dead weight, 2) maintenance cost free even in the severe sea conditions due to ex-tremely durable UFC material and 3) efficient and effective achievement of the mass production system due to assembly of standardized UFC members. We hope that this UFC technology would help the future development of concrete technology.

REFERENCE

JSCE 2004. Recommendation for Design and Construction Ul-tra High Strength Fiber Reinforced Concrete Structures-Draft. Concrete Library No 113.

Proceedings of FraMCoS-7, May 23-28, 2010

hThD ∇−= ),(J (1)

The proportionality coefficient D(h,T) is called moisture permeability and it is a nonlinear function of the relative humidity h and temperature T (Bažant & Najjar 1972). The moisture mass balance requires that the variation in time of the water mass per unit volume of concrete (water content w) be equal to the divergence of the moisture flux J

J•∇=∂

∂−

t

w (2)

The water content w can be expressed as the sum

of the evaporable water we (capillary water, water vapor, and adsorbed water) and the non-evaporable (chemically bound) water wn (Mills 1966, Pantazopoulo & Mills 1995). It is reasonable to assume that the evaporable water is a function of relative humidity, h, degree of hydration, αc, and degree of silica fume reaction, αs, i.e. we=we(h,αc,αs) = age-dependent sorption/desorption isotherm (Norling Mjonell 1997). Under this assumption and by substituting Equation 1 into Equation 2 one obtains

nscw

s

ew

c

ew

hh

Dt

h

h

ew

&&& ++∂

=∇•∇+∂

− αα

αα

)(

(3)

where ∂we/∂h is the slope of the sorption/desorption isotherm (also called moisture capacity). The governing equation (Equation 3) must be completed by appropriate boundary and initial conditions.

The relation between the amount of evaporable water and relative humidity is called ‘‘adsorption isotherm” if measured with increasing relativity humidity and ‘‘desorption isotherm” in the opposite case. Neglecting their difference (Xi et al. 1994), in the following, ‘‘sorption isotherm” will be used with reference to both sorption and desorption conditions. By the way, if the hysteresis of the moisture isotherm would be taken into account, two different relation, evaporable water vs relative humidity, must be used according to the sign of the variation of the relativity humidity. The shape of the sorption isotherm for HPC is influenced by many parameters, especially those that influence extent and rate of the chemical reactions and, in turn, determine pore structure and pore size distribution (water-to-cement ratio, cement chemical composition, SF content, curing time and method, temperature, mix additives, etc.). In the literature various formulations can be found to describe the sorption isotherm of normal concrete (Xi et al. 1994). However, in the present paper the semi-empirical expression proposed by Norling Mjornell (1997) is adopted because it

explicitly accounts for the evolution of hydration reaction and SF content. This sorption isotherm reads

( ) ( )( )

( ) ( )⎥⎥

⎢⎢

⎥⎥⎥

⎢⎢⎢

−∞

+

−∞

−=

1110

,1

110

11,

1,,

hcc

ge

scK

hcc

ge

scG

sch

ew

αα

αα

αα

αααα

(4)

where the first term (gel isotherm) represents the physically bound (adsorbed) water and the second term (capillary isotherm) represents the capillary water. This expression is valid only for low content of SF. The coefficient G1 represents the amount of water per unit volume held in the gel pores at 100% relative humidity, and it can be expressed (Norling Mjornell 1997) as

( ) ss

s

vgkc

c

c

vgk

scG αααα +=,1

(5)

where k

cvg and k

svg are material parameters. From the

maximum amount of water per unit volume that can fill all pores (both capillary pores and gel pores), one can calculate K1 as one obtains

( )1

110

110

11

22.0188.00

,1

−⎟⎠

⎞⎜⎝

⎛−∞

⎥⎥⎥

⎢⎢⎢

⎡⎟⎠

⎞⎜⎝

⎛−∞

−−+−

=

hcc

ge

hcc

geGs

ssc

w

scK

αα

αα

αα

αα

(6)

The material parameters k

cvg and k

svg and g1 can

be calibrated by fitting experimental data relevant to free (evaporable) water content in concrete at various ages (Di Luzio & Cusatis 2009b).

2.2 Temperature evolution

Note that, at early age, since the chemical reactions associated with cement hydration and SF reaction are exothermic, the temperature field is not uniform for non-adiabatic systems even if the environmental temperature is constant. Heat conduction can be described in concrete, at least for temperature not exceeding 100°C (Bažant & Kaplan 1996), by Fourier’s law, which reads

T∇−= λq (7)

where q is the heat flux, T is the absolute temperature, and λ is the heat conductivity; in this